Analysis I: Fourier Series and Partial Differential Equations
MAT 330

Spring 2010
MAT 330: Fourier Series and Partial Differential Equations Professor Sergiu Klainerman Problem Set 5
Rik Sengupta [email protected] March 30, 2010
1. Stein and Shakarchi, p. 162, problem 4 Bump functions. Examples of compactly supported functions in
Analysis I: Fourier Series and Partial Differential Equations
MAT 330

Spring 2010
MAT 330: Fourier Series and Partial Differential Equations Professor Sergiu Klainerman Problem Set 4
Rik Sengupta [email protected] March 1, 2010
1. Stein and Shakarchi, p. 124, problem 11 Show that if u(x, t) = (f Ht )(x) where Ht is the heat kernel
Analysis I: Fourier Series and Partial Differential Equations
MAT 330

Spring 2010
MAT 330: Fourier Series and Partial Differential Equations Professor Sergiu Klainerman Problem Set 6
Rik Sengupta [email protected] April 7, 2010
1. Stein and Shakarchi, p. 213, problem 3 We observed that the solution u(x, t) of the Cauchy problem fo
Analysis I: Fourier Series and Partial Differential Equations
MAT 330

Spring 2010
MAT 330: Fourier Series and Partial Differential Equations Professor Sergiu Klainerman Problem Set 7
Rik Sengupta [email protected] April 23, 2010
Hadamard's "Parties Finies" or PseudoFunctions, 1932
1. Let < 1 be a given real number and Z. Prove
Analysis I: Fourier Series and Partial Differential Equations
MAT 330

Spring 2010
MAT 330: Fourier Series and Partial Differential Equations Professor Sergiu Klainerman Problem Set 1
Rik Sengupta rsengupt @ princeton.edu February 6, 2010
1. Stein and Shakarchi, p. 24, problem 4 For z C, we define the complex exponential by ez = zn . n!
Analysis I: Fourier Series and Partial Differential Equations
MAT 330

Spring 2010
MAT 330: Fourier Series and Partial Differential Equations Professor Sergiu Klainerman Problem Set 2
Rik Sengupta [email protected] February 13, 2010
1. Stein and Shakarchi, p. 58, problem 1 Suppose f is 2periodic and integrable on any finite interv
Analysis I: Fourier Series and Partial Differential Equations
MAT 330

Spring 2010
MAT 330: Fourier Series and Partial Differential Equations Professor Sergiu Klainerman Problem Set 3
Rik Sengupta [email protected] February 24, 2010
1. Stein and Shakarchi, p. 88, problem 2 Prove that the vector space
2
(Z) is complete.
2
Solution.